In a lane-based evacuation network design problem that incorporates lane reversal and crossing elimination strategies, the network can be virtually decomposed to a number of roadway subnetworks and intersection subnetworks. Lane reversal and crossing elimination are implemented on roadway subnetworks and intersection subnetworks, respectively. Although this network decomposition mechanism naturally offers an appealing algorithmic approach for network solutions by relaxing the crossing elimination constraints, one needs to consider-from the solution feasibility perspective-the mutual connectivity requirements imposed by the two capacity-reallocation and connectivity- reallocation network settings simultaneously. This paper considers an intersection origin-destination flow distribution problem arising from the evacuation network design and outputs whether the crossing elimination constraints are satisfied or violated given a lane reversal solution. The main contribution of this work is to provide a condition of network flows sufficient for the existence and validity of the problem and develop an efficient simplexbased method to obtain solutions to the problem. Numerical examples are provided to illustrate the method's effectiveness and efficiency.